TSTP Solution File: NUM584+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : NUM584+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 11:57:06 EDT 2023
% Result : Theorem 7.40s 1.31s
% Output : Proof 7.40s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM584+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 16:24:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 7.40/1.31 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 7.40/1.31
% 7.40/1.31 % SZS status Theorem
% 7.40/1.31
% 7.40/1.31 % SZS output start Proof
% 7.40/1.31 Take the following subset of the input axioms:
% 7.40/1.31 fof(mDefSel, definition, ![W0, W1]: ((aSet0(W0) & aElementOf0(W1, szNzAzT0)) => ![W2]: (W2=slbdtsldtrb0(W0, W1) <=> (aSet0(W2) & ![W3]: (aElementOf0(W3, W2) <=> (aSubsetOf0(W3, W0) & sbrdtbr0(W3)=W1)))))).
% 7.40/1.31 fof(mDefSub, definition, ![W0_2]: (aSet0(W0_2) => ![W1_2]: (aSubsetOf0(W1_2, W0_2) <=> (aSet0(W1_2) & ![W2_2]: (aElementOf0(W2_2, W1_2) => aElementOf0(W2_2, W0_2)))))).
% 7.40/1.31 fof(mNATSet, axiom, aSet0(szNzAzT0) & isCountable0(szNzAzT0)).
% 7.40/1.31 fof(m__, conjecture, aElementOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), slbdtsldtrb0(xS, xK))).
% 7.40/1.31 fof(m__3418, hypothesis, aElementOf0(xK, szNzAzT0)).
% 7.40/1.31 fof(m__3435, hypothesis, aSubsetOf0(xS, szNzAzT0) & isCountable0(xS)).
% 7.40/1.31 fof(m__4007, hypothesis, sbrdtbr0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))=xK).
% 7.40/1.31 fof(m__4024, hypothesis, aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS)).
% 7.40/1.31
% 7.40/1.31 Now clausify the problem and encode Horn clauses using encoding 3 of
% 7.40/1.31 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 7.40/1.31 We repeatedly replace C & s=t => u=v by the two clauses:
% 7.40/1.31 fresh(y, y, x1...xn) = u
% 7.40/1.31 C => fresh(s, t, x1...xn) = v
% 7.40/1.31 where fresh is a fresh function symbol and x1..xn are the free
% 7.40/1.31 variables of u and v.
% 7.40/1.31 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 7.40/1.31 input problem has no model of domain size 1).
% 7.40/1.31
% 7.40/1.31 The encoding turns the above axioms into the following unit equations and goals:
% 7.40/1.31
% 7.40/1.31 Axiom 1 (m__3418): aElementOf0(xK, szNzAzT0) = true2.
% 7.40/1.31 Axiom 2 (mNATSet): aSet0(szNzAzT0) = true2.
% 7.40/1.31 Axiom 3 (m__3435_1): aSubsetOf0(xS, szNzAzT0) = true2.
% 7.40/1.31 Axiom 4 (mDefSub_3): fresh48(X, X, Y) = true2.
% 7.40/1.31 Axiom 5 (mDefSel_3): fresh210(X, X, Y, Z) = true2.
% 7.40/1.31 Axiom 6 (mDefSub_3): fresh49(X, X, Y, Z) = aSet0(Z).
% 7.40/1.31 Axiom 7 (m__4024): aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS) = true2.
% 7.40/1.31 Axiom 8 (m__4007): sbrdtbr0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))) = xK.
% 7.40/1.31 Axiom 9 (mDefSel): fresh55(X, X, Y, Z, W) = equiv3(Y, Z, W).
% 7.40/1.31 Axiom 10 (mDefSel): fresh54(X, X, Y, Z, W) = true2.
% 7.40/1.31 Axiom 11 (mDefSub_3): fresh49(aSubsetOf0(X, Y), true2, Y, X) = fresh48(aSet0(Y), true2, X).
% 7.40/1.31 Axiom 12 (mDefSel_3): fresh209(X, X, Y, Z, W, V) = fresh210(W, slbdtsldtrb0(Y, Z), W, V).
% 7.40/1.31 Axiom 13 (mDefSel_3): fresh208(X, X, Y, Z, W, V) = aElementOf0(V, W).
% 7.40/1.31 Axiom 14 (mDefSel): fresh55(aSubsetOf0(X, Y), true2, Y, Z, X) = fresh54(sbrdtbr0(X), Z, Y, Z, X).
% 7.40/1.31 Axiom 15 (mDefSel_3): fresh207(X, X, Y, Z, W, V) = fresh208(aSet0(Y), true2, Y, Z, W, V).
% 7.40/1.31 Axiom 16 (mDefSel_3): fresh207(equiv3(X, Y, Z), true2, X, Y, W, Z) = fresh209(aElementOf0(Y, szNzAzT0), true2, X, Y, W, Z).
% 7.40/1.31
% 7.40/1.31 Goal 1 (m__): aElementOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), slbdtsldtrb0(xS, xK)) = true2.
% 7.40/1.31 Proof:
% 7.40/1.31 aElementOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), slbdtsldtrb0(xS, xK))
% 7.40/1.31 = { by axiom 13 (mDefSel_3) R->L }
% 7.40/1.31 fresh208(true2, true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 4 (mDefSub_3) R->L }
% 7.40/1.31 fresh208(fresh48(true2, true2, xS), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 2 (mNATSet) R->L }
% 7.40/1.31 fresh208(fresh48(aSet0(szNzAzT0), true2, xS), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 11 (mDefSub_3) R->L }
% 7.40/1.31 fresh208(fresh49(aSubsetOf0(xS, szNzAzT0), true2, szNzAzT0, xS), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 3 (m__3435_1) }
% 7.40/1.31 fresh208(fresh49(true2, true2, szNzAzT0, xS), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 6 (mDefSub_3) }
% 7.40/1.31 fresh208(aSet0(xS), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 15 (mDefSel_3) R->L }
% 7.40/1.31 fresh207(true2, true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 10 (mDefSel) R->L }
% 7.40/1.31 fresh207(fresh54(xK, xK, xS, xK, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 8 (m__4007) R->L }
% 7.40/1.31 fresh207(fresh54(sbrdtbr0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), xK, xS, xK, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 14 (mDefSel) R->L }
% 7.40/1.31 fresh207(fresh55(aSubsetOf0(sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))), xS), true2, xS, xK, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 7 (m__4024) }
% 7.40/1.31 fresh207(fresh55(true2, true2, xS, xK, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.31 = { by axiom 9 (mDefSel) }
% 7.40/1.32 fresh207(equiv3(xS, xK, sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi)))), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.32 = { by axiom 16 (mDefSel_3) }
% 7.40/1.32 fresh209(aElementOf0(xK, szNzAzT0), true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.32 = { by axiom 1 (m__3418) }
% 7.40/1.32 fresh209(true2, true2, xS, xK, slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.32 = { by axiom 12 (mDefSel_3) }
% 7.40/1.32 fresh210(slbdtsldtrb0(xS, xK), slbdtsldtrb0(xS, xK), slbdtsldtrb0(xS, xK), sdtpldt0(xQ, szmzizndt0(sdtlpdtrp0(xN, xi))))
% 7.40/1.32 = { by axiom 5 (mDefSel_3) }
% 7.40/1.32 true2
% 7.40/1.32 % SZS output end Proof
% 7.40/1.32
% 7.40/1.32 RESULT: Theorem (the conjecture is true).
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